Question

what are the new vertices of a rectangle with original vertices at (1,2), (1,4), (4,4), and (4,2) when transformed to a similar figure by translating it 3 units right and 2 units down followed by a dilation of scale factor 2? a. (14,0),(8,0),(8,4),(14,4) b. (4,0),(4,2),(7,2),(7,0) c. (2,1),(2,3),(5,3),(5,1) d. (0,0),(0,2),(3,2),(3,0)

Explanation:

Step1: Apply translation

For a point $(x,y)$ translated 3 units right and 2 units down, the new - point is $(x + 3,y - 2)$.
For $(1,2)$: $(1+3,2 - 2)=(4,0)$; for $(1,4)$: $(1 + 3,4 - 2)=(4,2)$; for $(4,4)$: $(4+3,4 - 2)=(7,2)$; for $(4,2)$: $(4 + 3,2 - 2)=(7,0)$.

Step2: Apply dilation

For a dilation with a scale factor of 2, we multiply the coordinates of each translated point by 2.
For $(4,0)$: $(4\times2,0\times2)=(8,0)$; for $(4,2)$: $(4\times2,2\times2)=(8,4)$; for $(7,2)$: $(7\times2,2\times2)=(14,4)$; for $(7,0)$: $(7\times2,0\times2)=(14,0)$.

Answer:

A. (14,0),(8,0),(8,4),(14,4)